All of their main controllers are more or less iconic, but it's true that they choose to create a completely new controller each gen instead of improving the previous one. That's something I like though, which is why I prefer their approach.
I don't think it'll pose a problem for them, if anything it could be a strength. If they continue to provide backwards compatibility for their controllers, and improve support, gamers will get more options.

I may be wrong here but I'd say pretty much every one of Nintendo's controllers is iconic. Except for the pro controller, which is a piece of garbage.

SNES controller is so iconic, it's design is still used today.

ummm.... ahem.

All their controllers are iconic. From NES to the Wii. They don't have a standard design that transcend from one generation to another like the dualshock. But that's not a problem by any means. Look how horrendous the xbox controller was. It was an aberration. Microsoft just got right last gen with the X360 controller. 

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I think Gamecube Controller is iconic enough, Nintendo supported it for 3 generations, although it wasn't the primary controller for the last 2.

Why are some people naming controllers that Nintendo no longer produces or markets with their newest consoles? The OP used the word "have" instead of "had" and I'm pretty sure everyone knows what he means.

Honestly, though, I don't think it's much of a problem, but I do think it's a problem that you can buy a Nintendo system and then have to buy a different controller to get the "best experience". That's more complication than the average consumer wants.

They need the Pro Controller to be the basis for the rest of Nintendo conrollers.

If each gen was a modified improved gamecube controller I would cry with happiness.

Think of it as a woman. Cuteness only matters at first sight, the original xbox controller is something you try when you are drunk and end up keeping because it's confortable and then you realise that's all that matters in the end.